The goal of this project is to theoretically study the singularities near the moving contact line of a sliding droplet in relation to the problem of avalanche fronts in granular media. A droplet flowing down a window displays fascinating behaviours; involving bifurcations between singular shapes drop emission and coalescence, which have only recently been characterized experimentally. To describe these phenomena theoretically, one has to overcome a fundamental problem:
In classical hydrodynamics the flow naiad moving contact line develops infinite stress and energy dissipation.
It remains highly disputed how to couple the microscopes near the contact line to the large-scale dynamics of the drop. Though this has remained scarcely noticed up to now, the same singularity occurs at the tip of an avalanche ingrains flowing down an immobile pile. In this context, there have been promising advances to tie the microscopic grain dynamics near the avalanche front to the long-range fields. We will develop a common framework describing moving contact lines for both sliding drops and granular avalanches. We will employ so-called depth-averaged equations that have successfully been applied tcavalanches, and which are very similar to the lubrication theory for thin fluid layers. The latter will be used custody the drop shapes both analytically and numerically. To couple the continuum description to themicroscopies near the contact line we perform molecular dynamics simulations for both systems. In this multidisciplinary project, we benefit from the rapidly evolving fields of wetting, hydrodynamics and granular dynamics. The project provides a unique opportunity to combine these efforts; there will be a close collaboration with the granular lab at the Cole Normal Superior. For the applicant, the project allows to work with experts in both fields, to broaden his research on soft matter and statistical physics.
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